Blaze herself already is the Sol Dimension counterpart to Sonic. It's just that Blaze has one thing going for her that all of Sonic's other "counterparts" don't.
Metal Sonic is just evil robot Sonic. Shadow is just a darker (Super) Sonic. Silver tries to be "Future Sonic".
Aside from the fact that she runs fast, Blaze isn't just another "Sonic". Even in abilities. She's an actual counterpart and opposite, especially in personality. She's similar to him, but while there are things Sonic can do that Blaze can, there are things that Blaze can do that Sonic himself can't. The opposite is the case for every other character in the series. (Moreso now thanks to the Wisps. Damn aliens making other characters obsolete.)
Well, except maybe Espio, somewhat Amy and ironically enough, Silver. I hate Silver, though. Game Silver, anyway. I love everything about Archie Silver, though, since he started off like the Game version of himself but then learned from his mistakes, matured and bettered his skills and now is a competent, formidable and respectable character.
But yeah, if anything, Blaze is basically Shadow and Knuckles merged together and done right.